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Old 04-28-2012, 11:36 PM
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yaser yaser is offline
Join Date: Aug 2009
Location: Pasadena, California, USA
Posts: 1,478
Default Re: consistency issue on page 65

Originally Posted by dudefromdayton View Post
On the same page, I've been able to confirm the biases stated for H0 and H1, as well as the variance for H0. But for the variance of 1.69 for H1, I am obtaining 2.44 instead.

I have this problem whether I calculate the variance directly, or I calculate the out-of-sample error and subtract the bias.

It would be reassuring if I could show that my 2.44 figure is wrong, but as yet I have not succeeded.
This is curious. To calculate E_{\rm out}, you generate the two points x_1 and x_2 uniformly and independently, then connect them with a line. Since y_1=\sin(\pi x_1) and y_2=\sin(\pi x_2), you get the equation for the line (tangent to the sine if the two points coincide). You then integrate the difference squared between the line and the sine with respect to x (times the probability density which is {1\over 2}) to get E_{\rm out} for this data set, and double-integrate that with respect to x_1 and x_2 (times the probability density which is {1\over 2} for each variable) to get the expected E_{\rm out}.

Is this what you have done to come up with a numerical answer equal to E_{\rm out}=2.44+0.21?

Hint: It is much easier to Monte-Carlo.
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